The invention is based on a fuel injection pump of the type defined hereinafter. A fuel injection pump of this kind, known from German Offenlegungsschrift No. 23 53 737, has the object of shifting the onset of injection toward "late" as the load decreases. The control cross sections in the known fuel injection pump are embodied such that the injection onset is varied at low load by enabling a partial amount of the fuel pumped to drain out before the injection per se begins. In the most extreme case, this drainage can be effected up to a predetermined piston stroke, and within the limits of this condition the drainage is further controlled in that the instant during the pump piston stroke at which the outlet of the second relief conduit is opened is also determined by the position of a quantity adjusting device, which is embodied as an annular slide that is displaceable on the pump piston in accordance with load or rpm. The provision made in the known fuel injection pump is that in the idling range and in a portion of the partial load range, the piston stroke over the duration of which communication between the first and second relief conduits is established is fully exploited for relieving purposes. As the load increases, a limitation of this possible relief quantity is effected by means of opening the outlet of the second relief conduit later than otherwise. The effect, in this load range, is an increasingly earlier injection onset, and at full load operation or in the upper partial load range, any relief of the pump work chamber is precluded entirely, so that the pump piston can cause its entire full-load injection quantity to be injected, and no further shift of the injection onset toward "late" takes place.